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This paper studies the achievable rate region of the two-user multiple antenna broadcast channel with linear precoding. It consists of two parts: In the first part, the set of beam- forming vectors which achieve points on the Pareto boundary are characterized by a single real valued parameter per user. It is shown that a certain linear combination of the zero-forcing (ZF) beamforming vector and the maximum- ratio-transmission (MRT) beamforming vector can achieve all Pareto boundary points of the rate region. In the second part, an iterative algorithm is proposed to compute the maximum sum-rate. Based on the characterization of the Pareto boundary, we develop an outer approximation algorithm for monotonic optimization using polyblocks. Numerical examples provide comparisons between rate and capacity regions as well as between the maximum sum-rate and maximum- capacity operating points.